Typhoid was quite common in Victorian times - Prince Albert died of it in the 1860s, and my great x 2 grandmother Eliza died of it in 1875. Her death cert said she'd had it for 3 weeks which is interesting as it meant she had it when she went to register her husband Emmets Matthews death!
As far as I'm aware typhoid victims were buried - just as cholera, TB and other infectious diseases victims were. Understanding of the causes of these illnesses was poor - it was believed for a while that cholera was caused by bad smells. Only after the link with water was found did they start worrying about drainage, sewerage and clean water supplies.